Re: momentum conservation in collisions

[Jim Green <JMGreen@SISNA.COM>]

The following is a prime example of the use of fuzzy thinking and language
which is derived from  the "momentum " of history.  I think that the
insistence of using common but imprecise language leads one to this sort of
conundrum -- use the language if one insists but then deal with the
confusion -- in the minds of teacher and student alike:

>"How come energy can be dissipated (and usually is)
> during a collision but not momentum?" OR,

The energy of a system can be increased or decreased but not "disipated"


> "Why can
> energy either be dissipated within a system or to its
> surroundings, but momentum can ONLY be dissipated by

Energy does not "leak"

>friction. So the system energy is initially stored

Nor is it "stored"

> solely in the moving cart (as Ek). I believe there is
> only one mechanism for the transfer of both energy and

or "transfered"

> momentum within the system (ie, from cart 1 to cart
> 2). That mechanism is the force of the moving cart
> acting on the parked cart during the collision. The
> integral of this force with respect to time yields the
> momentum gain of the parked cart which is exactly
> equal to the momentum loss of the moving cart; ie,
> perfect conservation of momentum. The integral of this
> SAME FORCE with respect to distance yields the energy

No! It yields work done!

> gain of the parked cart which is equal to the energy
> loss of the moving cart

No! ... to the work done

> EXCEPT that a large portion of
> the energy is "spilled" in the process showing up as

"Spilled"!!!??? Now I am yelling at my monitor!

> Ediss at the expense of Ek. That is, the energy pie
> that was 100% Ek immediately prior to the collision is

"Pie"???  Energy is not a substance that is divied up in some obscure
way.  Each part of a system has the property of "energy' and the levels of
those energies can be changed.  If one totals up all the various "energies"
for an isolated system, that total will remain constant.  But totalling up
all the various energies is sometimes dificult --  and is made much more
difficult by language obfuscation.

> A related question came up in class today. We were
> modeling energy transfer by a pulse traveling through
> a medium consisting of point masses connected by
> springs.

If a teacher insists on talking about "energy transfer" without ample
explanation and caviates, s/he is just asking for trouble  -- and a
confused (or uneducated) class.

> The energy (amplitude) dissipates due to internal
> friction in the stretching and recovery of the springs

Now we have "energy" "dissipating" (which it does not do) but it now has an
"amplitude" -- and one wonders why the class may be confused.

> (as a mental model). BUT what happens to momentum?
> Isn't this a series of elastic collisions between
> point particles?

At this point we could start over and discuss the "substance" of momentum.

Jim Green
mailto:JMGreen@sisna.com
http://users.sisna.com/jmgreen